On the performance of voltage stepping for the simulation of adaptive, nonlinear integrate-and-fire neuronal networks

In traditional event-driven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrate-and-fire model. In a recent paper, Zheng, Tonnelier, and Martinez (2009) introduced an approximate event-driven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrate-and-fire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrate-and-fire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified time-stepping scheme of the Runge-Kutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity.